Scientific & Chemical
Fundamentals
Measurement, Conversions &
Calculations
Dr. Ron Rusay
© Copyright 2003-2010 R.J. Rusay
Measurement & Units
SI units & common units in General Chemistry
(Refer to Lab Manual)
1
• Quantitative vs. Qualitative
• MASS (Chem: gram; SI: kg)
• LENGTH (Chem: cm & others; SI: m)
• TEMPERATURE (Celsius & Kelvin; SI: K)
• VOLUME (Chem: mL; SI: Liter)
• CHEMICAL AMOUNT: Mole (mol)
© Copyright 1998-2010 R.J. Rusay
Units of Measure
Units
U.S.
SI
Chemistry
Mass (weight)
Pound (lb)
Kilogram (kg)
Volume
Gallon (gal)
u
Liter (L)
Temperature
Fahrenheit
(oF)
Mile (mi),
Feet(ft), Inches
(in)
Kelvin (K)
“ Gram”
(g, mg)
“ Liter”
(mL, L)
K & Celsius (oC)
Length
Time
Meter (m)
“ Meter”
(cm, mm, nm)
Second (s)
Second (s)
Mole (mol)
QUESTION
Identify the best match between the dimension or
quantity and its correct SI base unit.
A)
B)
C)
D)
E)
Dimension or Quantity
Mass
Length
Time
Temperature
Amount of substance
Unit
Gram
Kilometer
Minute
Celsius
Mole
Answer
Identify the best match between the dimension or
quantity and its correct SI base unit.
A)
B)
C)
D)
E)
Dimension or Quantity
Mass
Length
Time
Temperature
Amount of substance
Unit
Gram
Kilometer
Minute
Celsius
Mole
Mass and Volume Measurements:
Refer to Lab Manual
Mass Determination
(Weighing Devices: Balances)
Liquid Measurement Tools
QUESTION
Identify the best match between the dimension or
quantity and the unit that is most likely to be
measured in Chem 120 lab.
A)
B)
C)
D)
E)
Dimension or Quantity
Mass
Length
Volume
Temperature
Amount of substance
Unit
Kilogram
Meter
Milliliter
Fahrenheit
Megamole
Answer
Identify the best match between the dimension or
quantity and the unit that is most likely to be
measured in Chem 120 lab.
A)
B)
C)
D)
E)
Dimension or Quantity
Mass
Length
Volume
Temperature
Amount of substance
Unit
Kilogram
Meter
Milliliter
Fahrenheit
Megamole
Volumes of regular shapes
V=s3
h
V=lxwxh
01_05
1m3
Volume
1dm3= 1 L
1cm3= 1 mL
1 cm
1 cm
Numbers & Measurement
The Importance of Units

Measurement - quantitative observation
consisting of 2 parts
• Part 1 - number
• Part 2 - unit

Examples:
• 20 grams
• 6.63   joules / second
Scale: Size & Comparison
 Macroscopic
vs. Microscopic
 IBM financed Video:
http://www.wordwizz.com/imagendx.htm
How would you compare your lifespan?.. to that
of a dog? ….to the age of the earth?…How
about the age of mankind to that of all life?..
..the age of industrialized mankind to the age
of mankind?
Graphic Comparisons
QUESTION
Assume that the earth is 4.6 billion years old and
that your Chem 120 class’s average lifespan will
be 80 years. If the age of the earth is represented
by the face of a clock, how many seconds will the
80 years be relative to the earth’s age on the
clock?
A) 0.91 ms
B) 3.3 s
C) 6.6 s
D) 13 s
E) 2.5 Gs
Answer
Tomorrow
Assume that the earth is 4.6 billion years old and
that your Chem 120 class’s average lifespan will
be 80 years. If the age of the earth is represented
by the face of a clock, how many seconds will the
80 years be relative to the earth’s age on the
clock?
A) 0.91 ms
B) 3.3 s
C) 6.6 s
D) 13 s
E) 2.5 Gs
Powers of Ten:
Scale
Language describes scale (prefixes)
Shorthand Prefixes
QUESTION
Science, 317, 765-775,
(2007)
“The Electron Stopwatch”
A. 10x
An array of multilayer mirrors compresses
ultrabroadband laser pulses (orange beam).
The attosecond x-ray pulses allow the realtime observation of atomic-scale electron
motion. The previous spectroscopic method
was on a femtosecond scale, which was too
slow to capture the movement.
How many times faster is attosecond
spectroscopy compared to femtosecond
methods?
B. 100x
C. 1,000x
D. 1,000,000x
Answer
Science, 317, 765-775,
(2007)
“The Electron Stopwatch”
A. 10x
An array of multilayer mirrors compresses
ultrabroadband laser pulses (orange beam).
The attosecond x-ray pulses allow the realtime observation of atomic-scale electron
motion. The previous spectroscopic method
was on a femtosecond scale, which was too
slow to capture the movement.
How many times faster is attosecond
spectroscopy compared to femtosecond
methods?
B. 100x
10-15 / 10-18 =
C. 1,000x
D. 1,000,000x
Commonly used prefixes in
Chemistry
These should be known from memory.
QUESTION
Select the correct relationship between these
metric units of length or distance.
A) 1 km = 100 m
B) 1 mm = 10 cm
C) 1 nm = 109 m
D) 103 mm = 1 m
Answer
Select the correct relationship between these
metric units of length or distance.
A) 1 km = 100 m
B) 1 mm = 10 cm
C) 1 nm = 109 m
D) 103 mm = 1 m
QUESTION
Coincidentally, a U.S. nickel has a mass of approximately 5
grams. If you had one dollar’s worth of nickels in your jean’s
what would be the mass of the nickels in milligrams?
A.
B.
C.
D.
100 milligrams
50 milligrams
1,000 milligrams
100,000 milligrams
1000 milligrams (mg) = 1 gram (g)
Answer
Coincidentally, a U.S. nickel has a mass of approximately 5
grams. If you had one dollar’s worth of nickels in your jean’s
what would be the mass of the nickels in milligrams?
A.
B.
C.
D.
100 milligrams
50 milligrams
1,000 milligrams
100,000 milligrams
20 nickels make up one dollar, then one dollar’s worth of nickels would have a
mass of 5g x 20=100 grams. Next, the conversion between grams and milligrams
is done by multiplying by 1,000 (because there are 1,000 milligrams per 1 gram.)
Would the weight of the nickels pull your jean’s down off of
your waist?
Answer
Coincidentally, a U.S. nickel has a mass of approximately 5
grams. If you had one dollar’s worth of nickels in your jean’s
what would be the mass of the nickels in milligrams?
A.
B.
C.
D.
100 milligrams
50 milligrams
1,000 milligrams
100,000 milligrams
20 nickels make up one dollar, then one dollar’s worth of nickels would have a
mass of 5g x 20=100 grams. Next, the conversion between grams and milligrams
is done by multiplying by 1,000 (because there are 1,000 milligrams per 1 gram.)
Would the weight of the nickels pull your jean’s down off of
your waist?
Likely not. 100g = 100g/454 g/lb equals 0.22lb ~ the weight of a
quarter pounder
Scientific Notation &
Significant Digits
Scientific Notation: A single digit followed by a
decimal and a power of ten.
Examples: 2,345 mL and 0.002340 g
2,345 mL = 2.345 x 10 3mL 0.002340 g = 2.340 x 10 -3 g
Numbers
1
• Expressing a number correctly is determined
by the method used in the measurement!
• How many numbers should I include?
Significant Digits (Figures)
Consider: the exactness of the measured value
• Short Hand expression translates the
number: Scientific Notation
© Copyright 1998-2010 R.J. Rusay
QUESTION
Assume that the earth is 4.6 billion years old and
that your Chem 120 class’s average lifespan will
be 80 years. If the age of the earth is represented
by the face of a clock, how many seconds will the
80 years be relative to the earth’s age on the
clock?
A) 0.91 ms
C) 6.6 s
•
•
B) 3.3 s
D) 13 s
E) 2.5 Gs
After time expires, put your Group’s mathematical solution
for the question on the Blackboard.
Then, get a laptop from the balance room. Open a browser and
then open the course calendar page.
Answer
Assume that the earth is 4.6 billion years old and
that your Chem 120 class’s average lifespan will
be 80 years. If the age of the earth is represented
by the face of a clock, how many seconds will the
80 years be relative to the earth’s age on the
clock?
A) 0.91 ms
B) 3.3 s
C) 6.6 s
D) 13 s
E) 2.5 Gs
What is the length of the rod?
Different measurement tools give different numbers:
Which ruler is better?
? cm
4.2 - 4.3cm
? cm
4.24 - 4.25cm
What is the diameter of a circle?
All measuring devices are not the same, and the values
(numbers) that come from them indicate their limitations.
Is there a better instrument to use other than a ruler to
measure the diameter of the sphere?
Buret
08
mL
0
10
22.2 mL
20
30
40
50
What does each line represent?
1 mL
What can be estimated?
O.1 mL
Measurement Assignment
http://chemconnections.org/general/chem120/volume1.htm
Temperature Scales
Relative to Water
“Normal” Body Temperature
QUESTION
Dr. R. walks into class and claims, “It is very cold in here today. It
feels like 242 K.” If that were the temperature, would you agree
that you would feel cold? What would that be in Celsius degrees?
A.
B.
C.
D.
I agree, that would be 31°C.
I agree, that would be – 31°C.
I do not agree, that would be 31°C.
I do not agree, that would be 515°C.
Answer
Dr. R. walks into class and claims, “It is very cold in here today. It
feels like 242 K.” If that were the temperature, would you agree
that you would feel cold? What would that be in Celsius degrees?
A.
B.
C.
D.
I agree, that would be 31°C.
I agree, that would be – 31°C.
I do not agree, that would be 31°C.
I do not agree, that would be 515°C.
The formula to use is K = °C + 273.15. Rearranged to yield
K – 273.15 = °C.
Temperature
Reporting Numbers
Rules for Significant Digits (Figures)

Nonzero integers always count
as significant figures.
 3456
g has how many sig figs?
 4 sig figs.
• Expressed in scientific notation?
3.456 x 10 3 g
Reporting Numbers
Rules for Significant (Digits) Figures

Exact numbers (unit, conversion
or scale factors) can have an infinite
number of significant figures.
1
liter = 1,000. ml, exactly
1
inch = 2.54 cm, exactly
Zeros

Leading zeros do not count as
significant figures.

0.0486 mL has how many sig figs?
 3 sig figs.
• Number expressed in scientific
notation?
4.86 x 10 -2 mL
Zeros



Captive zeros always count as
significant figures.
16.07 cm has how many sig figs?
 4 sig figs.
Number expressed in scientific
1.607 x 10 1 cm
notation?
Zeros


Trailing zeros are significant only if
the number contains a decimal
point.
9.300 kg has how many sig figs?
 4 sig figs.
• Number expressed in scientific
9.300 kg
notation?
QUESTION
In which of these measured values are the zeros
not significant figures?
I) 0.0591 cm
II) 504 g
III) 2.70 m
IV) 5300 L
A) I and II
B) II and III
D) I, III, and IV
C) I and IV
E) II, III, and IV
Answer
In which of these measured values are the zeros
not significant figures?
I) 0.0591 cm
II) 504 g
III) 2.70 m
IV) 5300 L
A) I and II
B) II and III
D) I, III, and IV
C) I and IV
E) II, III, and IV
QUESTION
Which one of the following does NOT represent four significant
digits?
A.
B.
C.
D.
0.07100 mg
0.7100 mg
0.7010 mg
0.0710 mg
Answer
Which one of the following does NOT represent four significant
digits?
A.
B.
C.
D.
0.07100 mg
0.7100 mg
0.7010 mg
0.0710 mg
The zero in front of the decimal point is not a part of any
measurement, the next zero is a place holder, and the last zero
is part of the measurement and significant. Therefore 3 sig figs.
Mathematics & Arithmetic
1
• Relative to method(s) of measurement
• Short Hand expression: Scientific Notation
• Numbers : How many to include?
Quantitative vs. Qualitative
• Addition/Subtraction......
• Multiplication/Division.....
• What is “significant”?.....Rounding Off
• http:dbhs.wvusd.k12.ca.us/SigFigsFable.html
© Copyright 1998-2010 R.J. Rusay
Systematic Problem Solving
Dimensional/Unit Analysis: Conversions
Workshop
How many mL of milk are in a1/2 gallon carton?
0.50 gal
1 gal = 4 qt
? mL
1 qt = 946 mL
0.50 gal | 4 qt | 946 mL = ? mL
| 1 gal | 1 qt
Complete the following
Units & Conversions
Number
13,000,000,000 yrs.
Scientific Notation
10 yrs
1.3
x
10
________________
546
___________
mL
5.46 X 10 2 mL
______________
0.845
____________
kg __8.45 x 10 -1 kg___
Named unit
__? gigayears
13 Gyrs
0.546 Liters
0.546 L
_? grams__
845 g
Computational Rules
1
• Addition/Subtraction: Answer expressed
•
to the least number of decimal places of
the figures in the process
Multiplication/Division: Answer
expressed to the least number of
significant figures
© Copyright 1998-2010 R.J. Rusay
Addition
 Four
students were each asked to
measure a piece of wire and provide a
total length for the four pieces.
 Report the result correctly:
0.05 cm
12.01 cm
1.9 cm
+
2.386 cm
_______
16.346 cm
QUESTION
If you were unloading a 23.50 kg box of books from your car and
a “friend” added two more 482 gram chemistry books, how much
in kg and using the rules for significant digits, would you be
lifting?
A.
B.
C.
D.
23.98 kg
24.464 kg
24.46 kg
24.5 kg
Answer
If you were unloading a 23.50 kg box of books from your car and
a “friend” added two more 482 gram chemistry books, how much
in kg and using the rules for significant digits, would you be
lifting?
A.
B.
C.
D.
23.98 kg
24.464 kg
24.46 kg
24.5 kg
The 482 grams of mass must be doubled (to include both books) and
482 grams is 0.482 kg. When adding measurements the answer has
the same number of decimal places as the fewest decimal places in the
calculation. Therefore the answer has 2 decimal places.
Mathematical Processes:

Provide correct answers assuming each value (unit
omitted) is written with the correct number of sig figs:
12.01
x
1.90
_______ ______________
= 9.56370
2.386
12.01
x
1.90
_______ ______________
+ 0.05 = 9.61370
2.386
QUESTION
The average mass of a certain brand of vitamin C tablets is 253 mg.
What is the mass of three such tablets rounded to the proper
number of significant digits?
A.
B.
C.
D.
0.760 grams
0.759 grams
0.7590 grams
0.253 grams
Answer
The average mass of a certain brand of vitamin C tablets is 253 mg.
What is the mass of three such tablets rounded to the proper
number of significant digits?
A.
B.
C.
D.
0.760 grams
0.759 grams
0.7590 grams
0.253 grams
3 tablets  253 milligrams = 759 milligrams, then dividing by 1,000
converts the milligrams to grams. Note the three is a count of the
number of objects, not a measured quantity and 759 retains the same
number of significant digits as the least found in related
measurements.
Conversion Factor Method
(Dimensional Analysis)
1
• Qualitative Descriptions vs. Quantitative
• Use exact numbers / “scale factor” UNITS
• A Bookkeeping Method: Example Short”
5 ft___in
4
___
--------> ? m
• (1 ft = 12 in; 2.54 cm = 1 in; 100 cm = 1 m)
5
4
• ___ft
x 12 in/ft + ___in
= 64
___in
1.626
64
• ___in
x 2.54 cm/in x 1 m/100cm = ___m
162.6 cm
© Copyright 1998-2010 R.J. Rusay